Solution curves on a slope field with an equilibrium line

The question

Name: ______________________   Date: ____________   Solution curves on a slope field with an equilibrium line (9 points)

1. (a) On the slope field, sketch the solution curve through $(0, 3)$ and the solution curve through $(0, 1)$. [2 points]

2. (b) Write the equation of the constant solution to the differential equation. Explain why the solution curve through $(0, 1)$ stays below it. [2 points]

3. (c) Let $y = f(x)$ be the solution through $(0, 3)$. Find the value of $x$ in $(0, \pi)$ at which $f$ has a relative maximum. Justify your answer. [2 points]

4. (d) Find $y = f(x)$, the particular solution with $f(0) = 3$. [3 points]